Local extrema/ relative maxima and minima

No, that's not quite right.

The max at (-1, 20) is local, not absolute. (For example, for x = 6, y = 69, which is greater than your "absolute" maximum.)

Likewise the min at (3, -12) is local, not absolute. (For example, for x = -4, y = -61, which is less than your "absolute" minimum.

This function is unbounded above and below, so there is no absolute max or absolute min.

You have it backwards. The function has a local maximum at (-1, 20) and a local minimum at (3, -12). The function does not have an absolute minimum or maximum. It tends to infinity as x tends to infinity, and to -infinity as x tends to -infinity.

No, it doesn't have a local max/min..... the only thing that it has are absolute max and absolute min